Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-10T20:32:32.606Z Has data issue: false hasContentIssue false

Uniqueness and stability of the recovery of an absorbing obstacle from a knowledge of its scattering resonances

Published online by Cambridge University Press:  11 July 2007

C. Labreuche
Affiliation:
Thomson–CSF/LCR, Domaine de Corbeville, 91404 Orsay Cedex, France

Abstract

In a previous paper, I investigated the use (for the inverse scattering problem) of the resonant frequencies and the associated eigen far-fields. I showed that the shape of a sound soft obstacle is uniquely determined by a knowledge of one resonant frequency and one associated eigen far-field. Inverse obstacle scattering problems are ill-posed in the sense that a small error in the measurement may imply a large error in the reconstruction. This is contrary to the idea of continuity. I proved that, by adding some a priori information, the reconstruction becomes continuous. More precisely, continuity holds if we assume that the obstacle lies a fixed and known compact set.

The goal of this paper is to extend these results to the case of absorbing obstacles.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 2000

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)